The BBC's top radio broadcaster, John Humphrys, threatened to quit the Today programme yesterday after it cut a dramatic section of his interview with Rowan Williams, the Archbishop of Canterbury.

Dr Williams objected to being asked about the morality of the Iraq war, and his staff demanded that the offending portions be removed before the pre-recorded interview was aired.

To the anger of staff, the BBC agreed, plunging the Today programme into another Iraq row less than six months after it broadcast Andrew Gilligan's "sexed-up dossier" story.

The interview was recorded just before 7am. After questioning Dr Williams about the divisions in the Anglican Communion over homosexuality, Humphrys asked him whether the war in Iraq was "immoral".

A 12-second silence followed. Asked why he hesitated, Dr Williams said: "Immoral is a short word for a very, very long discussion."

When the interview was over, Dr Williams said he believed there had been an agreement not to talk about the war. The matter was referred to the programme editor, Kevin Marsh, who was not in the office. He agreed the disputed section should be removed.

But producers did not tell Humphrys, who told listeners just before the 8am news that they would hear Dr Williams's views on the Iraq war as well as the gay bishop row.

When he found out about the cut, Humphrys launched into a furious off-air tirade, part of which could be heard in the background to the news bulletin. Threatening to quit, he said it was the "best interview of my career" and castigated bosses for caving in. The 12-second silence, if broadcast, would have had a big impact. "In radio terms, it's an eternity," one BBC source said.

The BBC has already been accused of timidity this week for failing to broadcast Michael Crick's investigation into the arrangements for paying Betsy Duncan Smith, the wife of the Tory leader, for working as his secretary.

The incident has soured the already strained relations between Humphrys and Marsh: the presenter is reported to have been offered a lucrative contract outside the BBC.

It has also raised questions about the media strategy adopted by Dr Williams's staff. Many in the Church of England are increasingly concerned that his communications skills - one of his strengths and a reason for appointing him 15 months ago - have been undermined by his communications staff at Lambeth Palace, who are determined he should keep a low profile.

They have refused almost all interviews and contrived to ensure that Dr Williams's first foreign trip, to Africa last July, was not accompanied by the media and received no publicity in Britain.

A spokesman at Lambeth Palace said yesterday: "We are not offering our version of events or commenting on anything that is not in the public domain. You will have to speak to the Today programme."

The BBC said: "The archbishop insists that he agreed to the interview only on the understanding that it would be confined to the single subject of this week's Lambeth conference.

"The Today programme accepts that the archbishop thought the interview would be on the single subject, so in the interests of fair dealing, decided not to run that section of the interview which went beyond its main purpose."

· Catholic bishops renewed their attack on the BBC yesterday, saying its reputation for fairness and objectivity was "increasingly tarnished" by recent current affairs programmes. They accused "elements within the BBC" who, they claimed, were hostile to religion. The statement was issued through the Vatican press office, a tactic designed to give added impact.

The missing extract

John Humphrys: Can I turn this conversation to Iraq? Before you were enthroned as Archbishop of Canterbury, you said, you signed a statement published in the Tablet, that said the war was immoral. Is that still your view?

Rowan Williams: At the time of course when I signed that statement there was no war. We were considering what might happen. Since that time I have commented on the possible risks of going to war before war broke out.

I have attempted during the period of the war to respect what's going on and not to make idle or armchair pontifications about it. Since the war has drawn to a close of military operations, I have been reflecting on where we are now, and my view is still that there are major questions about that enterprise.

JH: Was it immoral?

(A 12-second pause)

RW: It seems to me that the action in Iraq was one around which there were so many questions about long-term results, about legal justification that I would find it very hard to give unqualified support to the rightness of that decision.

JH: You hesitated a very long time before you answered that, Archbishop.

RW: Immoral is a short word for a very, very long discussion.

JH: As Archbishop, do you not have an absolute responsibility as spiritual leader of this country to say very clearly, if we go to war, whether you believe that war is moral or not, and do you not have the sense that you are hedging a little here?

RW: No I don't, because I don't believe that the moral contribution that can be made by any spiritual leader is ever a matter of simply handing down something like the 10 commandments.

It's a matter of trying to understand more deeply what sort of moral choices others are having to face, assisting with all the resource that I can bring to that and of course trying to live with the decisions that they make.

I think it's something of a fallacy to suppose that moral leadership is always saying, "This is right, this is wrong," because that may be very satisfying but it may not necessarily change anything or move anything forward.